What is a Bit?

A bit is a discrete "piece" of information. It is a physical entity. In computers we encode this information as either voltage ON or voltage OFF.


Consider a coin. It has two information states Heads or Tails. So a sequence of bits can represent a series of successive coin tosses.

A mechanism, like a box that flips coins, which produces a series of bits, is sometimes called an information source. Even if this information source produces "noise" (e.g. random bits of information) it is still generating physical information.

Consider a coin that is flipped twice: What are the possible outcomes?

  1. HH
  2. HT
  3. TH
  4. TT

Four equally likely outcomes can be represented by two bits of individual information (e.g. H or T).



For three coin flips 8 different equally likely outcomes and three bits. So if something has N equally likely outcomes, it will take

b = log2 N

bits to represent this.

Powers of 2 table:


Now let's go back to the case of 3 bits that represent 8 equally likely outcomes.



The next step is to have "protocol" mapping onto the bits. That is, column A makes sense as a protocol while column B does not. This is precisely what the ASCII standard is. To represent a character (in the english language) by a unique pattern of bits.

In fact, it is a unique pattern of 8 bits and 8 bits make up a BYTE .

Each character then requires 1 BYTE of memory to be stored.

Atoms vs Bits


Atoms The "smallest" possible piece of matter (well not really but we won't worry about quarks here). Arrangements of atoms give us the periodic table of elements . You can regard this as a protocol.



Bits The smallest possible piece of information. By protocol (discussed above) we can define bits to represent larger pieces of information. The physics will enter into this when we figure out how to represent bits by electrons. Then you can transmit information!



Atoms and Bits are linked. Think about a book - it has a physical form which is composed of atoms but it contains information which is composed of bits.

In the coming decades, research at the quantum level will continue to benefit from the manipulation of single atoms and molecules through devices like optical traps. The necessary technological developments for that manipulation will allow physicists to treat atoms as "bits" of information for the purposes of quantum computing.The growth in our ability to manipulate bits in this century will affect society as much as our growth in our ability to maniuplate atoms did in the last century. That is, the information revolution is very similar to the industrial revolution.



Measuring Information:

  • 1 Byte = 8 bits
  • 1 Kilobyte = 1000 bytes = 1K
  • 1 Megabyte = 1000K = 1 meg
  • 1 Gigabyte = 1000meg = 1 Gig
  • 1 Terabyte = 1000Gigs = not yet a household term (but you can now hold a couple of terabytes in your hand)

Some equivalencies:

  • A single spaced page of text = 2K
  • 1 3"x5" full color picture = 80K
  • A four minute song on a CD = 35 Megs which is why Napster melted networks initially
  • A full length movie (uncompressed) = 150 Gigs compression gets it down to 7 Gigs which is the DVD format.

Generally storage size for images can be calculated as follows:

Storage in Megabytes = number of pixels x bits per pixel.

So, supposed you have a 1 megapixel camera and each pixel contains 16 bits of information.

Total image size is then 1 million x 16 bits = 16 million bits.

8 bits per byte so that is 2 million bytes or 2 Megabytes.


Suppose you have a 10 million pixel camera that takes 24 frames per second at 24 bits (true color) per pixel and you shoot a 30 second movie. What is the size?

  • 10 million pixels * 24 bits per pixel = 240 million mega bits = 30 Megabytes per frame
  • 24 frames per second = 24 x 30 = 720 Megabytes per second
  • 30 seconds: = 720 * 30 = 21,600 Megabytes = 21.6 Gigabytes


Wireless network speeds:

On any shared wireless network (like the one in this room) your data transfer speed will likely never be more than 20 Megabits per second = 2.5 Megabytes per second.

How many seconds would it take to upload your 21.6 Gbyte movie?

A long time: 21,600/2,5 = 8640 seconds = 2.4 hours.

The basic point is that it took you 30 seconds to make the information but 2.4 hoursor 8640/30 ~ 300 times longer to disseminate it. This is the essence of the information overload problem.



Currently Astronomers are building the the largest digital camera ever constructed and to be put in a location like this:



Camera size is 3.2 BILLION (Giga) pixels. Each single image is 12.8 GigaBytes. 4 images per minute taken = 50 Gigs per minute or 3 Terabytes (TB) per hour.

If this detector came ON line today, the data would simply be archived and never even looked at ...